Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
201
If two circles touch each other externally and their radii are 5 cm and 3 cm, what is the distance between their centers?
Answer:
8 cm
When two circles touch each other externally, the distance between their centers is simply the sum of their radii. Distance = r1 + r2 = 5 cm + 3 cm = 8 cm.
202
What is the angle subtended by a semicircle at its center?
Answer:
180 degrees
A full circle subtends an angle of 360 degrees at its center. A semicircle is exactly half of a circle, so the angle it subtends at the center is 360 / 2 = 180 degrees (a straight angle).
203
If the area of a circle is 154 cm², find its circumference. (Use π ≈ 22/7)
Answer:
44 cm
Area = π * r², so 154 = (22/7) * r². Thus, r² = 154 * (7/22) = 7 * 7 = 49, making r = 7 cm. The circumference C = 2 * π * r = 2 * (22/7) * 7 = 44 cm.
204
A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the center of the circle.
Answer:
6 cm
A perpendicular drawn from the center to a chord bisects the chord. This creates a right-angled triangle where the hypotenuse is the radius (10), and one leg is half the chord length (8). Using Pythagoras: d² + 8² = 10², so d² + 64 = 100, meaning d² = 36. The distance d = 6 cm.
205
If the circumference of a circle is 132 cm, what is its radius? (Use π ≈ 22/7)
Answer:
21 cm
The formula for circumference is C = 2 * π * r. We have 132 = 2 * (22/7) * r. This simplifies to 132 = (44/7) * r. To find r, multiply both sides by 7/44: r = 132 * (7/44) = 3 * 7 = 21 cm.
206
Find the length of an arc of a circle with radius 21 cm corresponding to a central angle of 120 degrees. (Use π ≈ 22/7)
Answer:
44 cm
The length of an arc is given by the formula L = (θ / 360) * 2 * π * r. Substituting the values: L = (120 / 360) * 2 * (22/7) * 21 = (1/3) * 2 * 22 * 3 = 44 cm.
207
What is the area of a sector of a circle with radius 6 cm and central angle 60 degrees? (Leave in terms of π)
Answer:
6π cm²
The formula for the area of a sector is (θ / 360) * π * r². Substituting the values: Area = (60 / 360) * π * 6² = (1/6) * π * 36 = 6π cm².
208
Find the area of a circle with a diameter of 20 cm. (Use π ≈ 3.14)
Answer:
314 cm²
If the diameter is 20 cm, the radius (r) is 10 cm. The area of a circle is A = π * r². Substituting the values: A = 3.14 * (10)² = 3.14 * 100 = 314 cm².
209
What is the circumference of a circle with a radius of 14 cm? (Use π ≈ 22/7)
Answer:
88 cm
The circumference of a circle is calculated using the formula C = 2 * π * r. Substituting the values: C = 2 * (22/7) * 14 = 2 * 22 * 2 = 88 cm.
210
Which polygon has the same number of diagonals as its sides?
Answer:
Pentagon
We need n(n - 3) / 2 = n. Since a polygon must have n >= 3, we can divide both sides by n, giving (n - 3) / 2 = 1. Therefore, n - 3 = 2, which means n = 5. A pentagon has 5 sides and 5 diagonals.